Problem: Drazil likes heap very much. So he created a problem with heap:

There is a max heap with a height h implemented on the array. The details of this heap are the following:

This heap contains exactly 2^h - 1 distinct positive non-zero integers. All integers are distinct. These numbers are stored in the array a indexed from 1 to 2^h-1. For any 1 < i < 2^h, a[i] < a[\left ⌊{i/2}\right ⌋].

Now we want to reduce the height of this heap such that the height becomes g with exactly 2^g-1 numbers in heap. To reduce the height, we should perform the following action 2^h-2^g times:

Choose an index i, which contains an element and call the following function f in index i:

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Note that we suppose that if a[i]=0, then index i don't contain an element.

After all operations, the remaining 2^g-1 element must be located in indices from 1 to 2^g-1. Now Drazil wonders what's the minimum possible sum of the remaining 2^g-1 elements. Please find this sum and find a sequence of the function calls to achieve this value.

Input

The first line of the input contains an integer t (1 ≤ t ≤ 70 000): the number of test cases.

Each test case contain two lines. The first line contains two integers h and g (1 ≤ g < h ≤ 20). The second line contains n = 2^h-1 distinct positive integers a[1], a[2], …, a[n] (1 ≤ a[i] < 2^{20}). For all i from 2 to 2^h - 1, a[i] < a[\left ⌊{i/2}\right ⌋].

The total sum of n is less than 2^{20}.

Output

For each test case, print two lines.

The first line should contain one integer denoting the minimum sum after reducing the height of heap to g. The second line should contain 2^h - 2^g integers v_1, v_2, …, v_{2^h-2^g}. In i-th operation f(v_i) should be called.

Example

Input


2
3 2
7 6 3 5 4 2 1
3 2
7 6 5 4 3 2 1


Output


10
3 2 3 1
8
2 1 3 1

Solution (in JAVA):

Solution:
//stan hu tao
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import java.util.*;
import java.io.*;
import java.math.*;

public class x1329C
{
    public static void main(String hi[]) throws Exception
    {
        FastScanner infile = new FastScanner();
        int T = infile.nextInt();
        StringBuilder sb = new StringBuilder();
        while(T-->0)
        {
            int N = infile.nextInt();
            int M = infile.nextInt();
            int[] arr = new int[1<<N];
            int K = (1<<N);
            for(int i=1; i < K; i++)
                arr[i] = infile.nextInt();
            long res = 0L;
            ArrayList<Integer> ls = new ArrayList<Integer>();
            for(int x: arr)
                res += x;
            int operations = (1<<N)-(1<<M);
            int curr = 1;
            while(operations > 0)
            {
                int deleted = -1;
                int x = curr;
                while(true)
                {
                    if(x*2+1 >= K)
                    {
                        deleted = x;
                        break;
                    }
                    if(arr[x*2] > arr[x*2+1])
                        x *= 2;
                    else if(arr[x*2] < arr[x*2+1])
                        x = x*2+1;
                    else
                    {
                        deleted = x;
                        break;
                    }
                }
                if(deleted >= 1<<M)
                {
                    res -= arr[curr];
                    ls.add(curr);
                    x = curr;
                    while(true)
                    {
                        if(x*2+1 >= K)
                        {
                            arr[x] = 0;
                            break;
                        }
                        if(arr[x*2] > arr[x*2+1])
                        {
                            arr[x] = arr[x*2];
                            x *= 2;
                        }
                        else if(arr[x*2] < arr[x*2+1])
                        {
                            arr[x] = arr[x*2+1];
                            x = x*2+1;
                        }
                        else
                        {
                            arr[x] = 0;
                            break;
                        }
                    }
                    operations--;
                }
                else
                    curr++;
            }
            sb.append(res+"\n");
            for(int x: ls)
                sb.append(x+" ");
            sb.append("\n");
        }
        System.out.print(sb);
    }
    static boolean debug = true;
    public static void print(int[] arr)
    {
        //for debugging only
        for(int x: arr)
            System.out.print(x+" ");
        System.out.println();
    }
    public static void print(ArrayList<Integer> arr)
    {
        //for debugging only
        for(int x: arr)
            System.out.print(x+" ");
        System.out.println();
    }
}
/*
1
3 2
7 6 3 5 4 2 1

 */
class FastScanner
{
    private int BS = 1 << 16;
    private char NC = (char) 0;
    private byte[] buf = new byte[BS];
    private int bId = 0, size = 0;
    private char c = NC;
    private double cnt = 1;
    private BufferedInputStream in;

    public FastScanner() {
        in = new BufferedInputStream(System.in, BS);
    }

    public FastScanner(String s) {
        try {
            in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
        } catch (Exception e) {
            in = new BufferedInputStream(System.in, BS);
        }
    }

    private char getChar() {
        while (bId == size) {
            try {
                size = in.read(buf);
            } catch (Exception e) {
                return NC;
            }
            if (size == -1) return NC;
            bId = 0;
        }
        return (char) buf[bId++];
    }

    public int nextInt() {
        return (int) nextLong();
    }

    public int[] nextInts(int N) {
        int[] res = new int[N];
        for (int i = 0; i < N; i++) {
            res[i] = (int) nextLong();
        }
        return res;
    }

    public long[] nextLongs(int N) {
        long[] res = new long[N];
        for (int i = 0; i < N; i++) {
            res[i] = nextLong();
        }
        return res;
    }

    public long nextLong() {
        cnt = 1;
        boolean neg = false;
        if (c == NC) c = getChar();
        for (; (c < '0' || c > '9'); c = getChar()) {
            if (c == '-') neg = true;
        }
        long res = 0;
        for (; c >= '0' && c <= '9'; c = getChar()) {
            res = (res << 3) + (res << 1) + c - '0';
            cnt *= 10;
        }
        return neg ? -res : res;
    }

    public double nextDouble() {
        double cur = nextLong();
        return c != '.' ? cur : cur + nextLong() / cnt;
    }

    public double[] nextDoubles(int N) {
        double[] res = new double[N];
        for (int i = 0; i < N; i++) {
            res[i] = nextDouble();
        }
        return res;
    }

    public String next() {
        StringBuilder res = new StringBuilder();
        while (c <= 32) c = getChar();
        while (c > 32) {
            res.append(c);
            c = getChar();
        }
        return res.toString();
    }

    public String nextLine() {
        StringBuilder res = new StringBuilder();
        while (c <= 32) c = getChar();
        while (c != '\n') {
            res.append(c);
            c = getChar();
        }
        return res.toString();
    }

    public boolean hasNext() {
        if (c > 32) return true;
        while (true) {
            c = getChar();
            if (c == NC) return false;
            else if (c > 32) return true;
        }
    }
}